Download or read book Radial Basis Functions written by Martin D. Buhmann and published by Cambridge University Press. This book was released on 2003-07-03 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author's aim is to give a thorough treatment from both the theoretical and practical implementation viewpoints. For example, he emphasises the many positive features of radial basis functions such as the unique solvability of the interpolation problem, the computation of interpolants, their smoothness and convergence and provides a careful classification of the radial basis functions into types that have different convergence

Download or read book Fast Radial Basis Functions for Engineering Applications written by Marco Evangelos Biancolini and published by Springer. This book was released on 2018-03-29 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the first “How To” guide to the use of radial basis functions (RBF). It provides a clear vision of their potential, an overview of ready-for-use computational tools and precise guidelines to implement new engineering applications of RBF. Radial basis functions (RBF) are a mathematical tool mature enough for useful engineering applications. Their mathematical foundation is well established and the tool has proven to be effective in many fields, as the mathematical framework can be adapted in several ways. A candidate application can be faced considering the features of RBF: multidimensional space (including 2D and 3D), numerous radial functions available, global and compact support, interpolation/regression. This great flexibility makes RBF attractive – and their great potential has only been partially discovered. This is because of the difficulty in taking a first step toward RBF as they are not commonly part of engineers’ cultural background, but also due to the numerical complexity of RBF problems that scales up very quickly with the number of RBF centers. Fast RBF algorithms are available to alleviate this and high-performance computing (HPC) can provide further aid. Nevertheless, a consolidated tradition in using RBF in engineering applications is still missing and the beginner can be confused by the literature, which in many cases is presented with language and symbolisms familiar to mathematicians but which can be cryptic for engineers. The book is divided in two main sections. The first covers the foundations of RBF, the tools available for their quick implementation and guidelines for facing new challenges; the second part is a collection of practical RBF applications in engineering, covering several topics, including response surface interpolation in n-dimensional spaces, mapping of magnetic loads, mapping of pressure loads, up-scaling of flow fields, stress/strain analysis by experimental displacement fields, implicit surfaces, mesh to cad deformation, mesh morphing for crack propagation in 3D, ice and snow accretion using computational fluid dynamics (CFD) data, shape optimization for external aerodynamics, and use of adjoint data for surface sculpting. For each application, the complete path is clearly and consistently exposed using the systematic approach defined in the first section.

Download or read book Spherical Radial Basis Functions Theory and Applications written by Simon Hubbert and published by Springer. This book was released on 2015-05-13 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first to be devoted to the theory and applications of spherical (radial) basis functions (SBFs), which is rapidly emerging as one of the most promising techniques for solving problems where approximations are needed on the surface of a sphere. The aim of the book is to provide enough theoretical and practical details for the reader to be able to implement the SBF methods to solve real world problems. The authors stress the close connection between the theory of SBFs and that of the more well-known family of radial basis functions (RBFs), which are well-established tools for solving approximation theory problems on more general domains. The unique solvability of the SBF interpolation method for data fitting problems is established and an in-depth investigation of its accuracy is provided. Two chapters are devoted to partial differential equations (PDEs). One deals with the practical implementation of an SBF-based solution to an elliptic PDE and another which describes an SBF approach for solving a parabolic time-dependent PDE, complete with error analysis. The theory developed is illuminated with numerical experiments throughout. Spherical Radial Basis Functions, Theory and Applications will be of interest to graduate students and researchers in mathematics and related fields such as the geophysical sciences and statistics.

Download or read book Recent Advances in Radial Basis Function Collocation Methods written by Wen Chen and published by Springer Science & Business Media. This book was released on 2013-11-09 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book surveys the latest advances in radial basis function (RBF) meshless collocation methods which emphasis on recent novel kernel RBFs and new numerical schemes for solving partial differential equations. The RBF collocation methods are inherently free of integration and mesh, and avoid tedious mesh generation involved in standard finite element and boundary element methods. This book focuses primarily on the numerical algorithms, engineering applications, and highlights a large class of novel boundary-type RBF meshless collocation methods. These methods have shown a clear edge over the traditional numerical techniques especially for problems involving infinite domain, moving boundary, thin-walled structures, and inverse problems. Due to the rapid development in RBF meshless collocation methods, there is a need to summarize all these new materials so that they are available to scientists, engineers, and graduate students who are interest to apply these newly developed methods for solving real world’s problems. This book is intended to meet this need. Prof. Wen Chen and Dr. Zhuo-Jia Fu work at Hohai University. Prof. C.S. Chen works at the University of Southern Mississippi.

Download or read book Construction of Global Lyapunov Functions Using Radial Basis Functions written by Peter Giesl and published by Springer. This book was released on 2007-04-11 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: The basin of attraction of an equilibrium of an ordinary differential equation can be determined using a Lyapunov function. A new method to construct such a Lyapunov function using radial basis functions is presented in this volume intended for researchers and advanced students from both dynamical systems and radial basis functions. Besides an introduction to both areas and a detailed description of the method, it contains error estimates and many examples.

Download or read book Radial Basis Function Networks 2 written by and published by . This book was released on 2001 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Radial Basis Function Neural Networks with Sequential Learning written by N. Sundararajan and published by World Scientific. This book was released on 1999 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: A review of radial basis founction (RBF) neural networks. A novel sequential learning algorithm for minimal resource allocation neural networks (MRAN). MRAN for function approximation & pattern classification problems; MRAN for nonlinear dynamic systems; MRAN for communication channel equalization; Concluding remarks; A outline source code for MRAN in MATLAB; Bibliography; Index.

Download or read book New Developments in Approximation Theory written by Manfred W. Müller and published by Springer. This book was released on 2012-12-06 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: A collection of papers by international contributors describing new developments in the fields of univariate and multivariate approximation theory. This research has applications in areas such as computer-aided geometric design, as applied in engineering and medical technology (e.g. computerized tomography).

Download or read book EEG Brain Signal Classification for Epileptic Seizure Disorder Detection written by Sandeep Kumar Satapathy and published by Academic Press. This book was released on 2019-02-10 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: EEG Brain Signal Classification for Epileptic Seizure Disorder Detection provides the knowledge necessary to classify EEG brain signals to detect epileptic seizures using machine learning techniques. Chapters present an overview of machine learning techniques and the tools available, discuss previous studies, present empirical studies on the performance of the NN and SVM classifiers, discuss RBF neural networks trained with an improved PSO algorithm for epilepsy identification, and cover ABC algorithm optimized RBFNN for classification of EEG signal. Final chapter present future developments in the field. This book is a valuable source for bioinformaticians, medical doctors and other members of the biomedical field who need the most recent and promising automated techniques for EEG classification. Explores machine learning techniques that have been modified and validated for the purpose of EEG signal classification using Discrete Wavelet Transform for the identification of epileptic seizures Encompasses machine learning techniques, providing an easily understood resource for both non-specialized readers and biomedical researchers Provides a number of experimental analyses, with their results discussed and appropriately validated

Download or read book Neural Networks and Soft Computing written by Leszek Rutkowski and published by Springer Science & Business Media. This book was released on 2013-03-20 with total page 935 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents new trends and developments in soft computing techniques. Topics include: neural networks, fuzzy systems, evolutionary computation, knowledge discovery, rough sets, and hybrid methods. It also covers various applications of soft computing techniques in economics, mechanics, medicine, automatics and image processing. The book contains contributions from internationally recognized scientists, such as Zadeh, Bubnicki, Pawlak, Amari, Batyrshin, Hirota, Koczy, Kosinski, Novák, S.-Y. Lee, Pedrycz, Raudys, Setiono, Sincak, Strumillo, Takagi, Usui, Wilamowski and Zurada. An excellent overview of soft computing methods and their applications.

Download or read book Meshfree Approximation Methods with MATLAB written by Gregory E. Fasshauer and published by World Scientific. This book was released on 2007 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: Meshfree approximation methods are a relatively new area of research. This book provides the salient theoretical results needed for a basic understanding of meshfree approximation methods. It places emphasis on a hands-on approach that includes MATLAB routines for all basic operations.

Download or read book Scattered Data Approximation written by Holger Wendland and published by Cambridge University Press. This book was released on 2004-12-13 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many practical applications require the reconstruction of a multivariate function from discrete, unstructured data. This book gives a self-contained, complete introduction into this subject. It concentrates on truly meshless methods such as radial basis functions, moving least squares, and partitions of unity. The book starts with an overview on typical applications of scattered data approximation, coming from surface reconstruction, fluid-structure interaction, and the numerical solution of partial differential equations. It then leads the reader from basic properties to the current state of research, addressing all important issues, such as existence, uniqueness, approximation properties, numerical stability, and efficient implementation. Each chapter ends with a section giving information on the historical background and hints for further reading. Complete proofs are included, making this perfectly suited for graduate courses on multivariate approximation and it can be used to support courses in computer-aided geometric design, and meshless methods for partial differential equations.

Download or read book Handbook of Geomathematics written by Willi Freeden and published by Springer. This book was released on 2010-10-20 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the last three decades geosciences and geo-engineering were influenced by two essential scenarios: First, the technological progress has changed completely the observational and measurement techniques. Modern high speed computers and satellite based techniques are entering more and more all geodisciplines. Second, there is a growing public concern about the future of our planet, its climate, its environment, and about an expected shortage of natural resources. Obviously, both aspects, viz. efficient strategies of protection against threats of a changing Earth and the exceptional situation of getting terrestrial, airborne as well as spaceborne data of better and better quality explain the strong need of new mathematical structures, tools, and methods. Mathematics concerned with geoscientific problems, i.e., Geomathematics, is becoming increasingly important. The ‘Handbook Geomathematics’ as a central reference work in this area comprises the following scientific fields: (I) observational and measurement key technologies (II) modelling of the system Earth (geosphere, cryosphere, hydrosphere, atmosphere, biosphere) (III) analytic, algebraic, and operator-theoretic methods (IV) statistical and stochastic methods (V) computational and numerical analysis methods (VI) historical background and future perspectives.

Download or read book Kernel based Approximation Methods using MATLAB written by Gregory Fasshauer and published by World Scientific Publishing Company. This book was released on 2015-07-30 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: In an attempt to introduce application scientists and graduate students to the exciting topic of positive definite kernels and radial basis functions, this book presents modern theoretical results on kernel-based approximation methods and demonstrates their implementation in various settings. The authors explore the historical context of this fascinating topic and explain recent advances as strategies to address long-standing problems. Examples are drawn from fields as diverse as function approximation, spatial statistics, boundary value problems, machine learning, surrogate modeling and finance. Researchers from those and other fields can recreate the results within using the documented MATLAB code, also available through the online library. This combination of a strong theoretical foundation and accessible experimentation empowers readers to use positive definite kernels on their own problems of interest.

Download or read book Algorithms for Approximation written by J. C. Mason and published by Oxford University Press, USA. This book was released on 1987 with total page 732 pages. Available in PDF, EPUB and Kindle. Book excerpt: The term "approximation" here refers to the approximation of functions and data by simple functions. Emphasizing the development of useful algorithms and practical applications in defense and industry, the papers cover topics such as multivariate interpolation, optimization methods, constrained problems, spline fitting, data modelling, and applications in microwave measurement, isotropic antennas, sound measurement, and digitized contours. Includes a substantial catalog of existing algorithms. No index. Annotation copyrighted by Book News, Inc., Portland, OR

Download or read book A Primer on Radial Basis Functions with Applications to the Geosciences written by Bengt Fornberg and published by SIAM. This book was released on 2015-09-30 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: Adapted from a series of lectures given by the authors, this monograph focuses on radial basis functions (RBFs), a powerful numerical methodology for solving PDEs to high accuracy in any number of dimensions. This method applies to problems across a wide range of PDEs arising in fluid mechanics, wave motions, astro- and geosciences, mathematical biology, and other areas and has lately been shown to compete successfully against the very best previous approaches on some large benchmark problems. Using examples and heuristic explanations to create a practical and intuitive perspective, the authors address how, when, and why RBF-based methods work. The authors trace the algorithmic evolution of RBFs, starting with brief introductions to finite difference (FD) and pseudospectral (PS) methods and following a logical progression to global RBFs and then to RBF-generated FD (RBF-FD) methods. The RBF-FD method, conceived in 2000, has proven to be a leading candidate for numerical simulations in an increasingly wide range of applications, including seismic exploration for oil and gas, weather and climate modeling, and electromagnetics, among others. This is the first survey in book format of the RBF-FD methodology and is suitable as the text for a one-semester first-year graduate class.

Download or read book Artificial Neural Networks for Speech and Vision written by Richard J. Mammone and published by Kluwer Academic Publishers. This book was released on 1994 with total page 616 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents some of the most promising current research in the design and training of artificial neural networks (ANNs) with applications in speech and vision, as reported by the investigators themselves. The volume is divided into three sections. The first gives an overview of the general field of ANN.